Colour Polymorphic Spiders and Range Size
Fabian C. Salgado-Roa
2023-10-17
1 Load packages and functions
1.1 Packages
library(ape)
library(phangorn)
library(caper)
library(tidyverse)
library(ggtree)
library(picante)
library(brms)
library(phangorn)
library(phytools)
library(treeio)
library(MASS)
library(car)
library(corrplot)
library(emmeans)
library(broom)
library(ggdist)
library(tidybayes)
library(raster)
library(sf)
library(exactextractr)
library(performance)1.2 Functions
##Check ultrametric and/or fix
check_and_fix_ultrametric <- function(phy){
if (!is.ultrametric(phy)){
vv <- vcv.phylo(phy)
dx <- diag(vv)
mxx <- max(dx) - dx
for (i in 1:length(mxx)){
phy$edge.length[phy$edge[,2] == i] <- phy$edge.length[phy$edge[,2] == i] + mxx[i]
}
if (!is.ultrametric(phy)){
stop("Ultrametric fix failed\n")
}
}
return(phy)
}
##Removed duplicated tips
remove_duplicate_tips<-function(tree){
for(spe in unique(tree$tip.label)){
pos<-grep(paste("\\b",spe,"\\b",sep=""),tree$tip.label)
if(length(pos)>1){
rem<-pos[2:length(pos)]
tree<-ape::drop.tip(phy=tree,tip=rem)
}
}
return(tree)
}
## Function for renaming tips
rename.tips.phylo <- function(tree, names) {
tree$tip.label <- names
return(tree)
}
#Stardarize variables
standard_varibles<-function(frame_data){
for(nom in names(frame_data)){
frame_data<-data.frame(frame_data)
if(class(frame_data[,nom])!="numeric"){next}
frame_data[,nom]<-scale(frame_data[,nom])[,1]
}
return(frame_data)
}
#standarize single variables
scale_single <- function(x){
(x - mean(x, na.rm=TRUE)) / sd(x, na.rm=TRUE)
}
#Standard error function
se <- function(x) sd(x)/sqrt(length(x))
#Mean function
meanfun <- function(data, i){
d <- data[i, ]
return(mean(d))
}
#Variation coefficient
var_coef <- function(x, na.rm = FALSE) {
sd(x, na.rm=na.rm) / mean(x, na.rm=na.rm)
}2 Phylogeny setting
We are going to load the phylogenies of the two main families (Araneidae and Theridiidae) obtained in BEAST to removed duplicated tips and prune some outgroups to generate a single phylogeny for further analyses.
2.1 Araneidae phylogeny
#Load Araneidae tree
mcc_tree<-read.nexus("araneidae_new_final.tre")
#load fixed tip names
nam_tree<-read_csv("tip_names_araneidae.csv",col_names=T)
mcc_tree$tip.label<-nam_tree$corrected_name
###Remove repeated tips
tree_removedTips<-remove_duplicate_tips(mcc_tree)
##Remove tips to mix with Theridiidae tree
core<-extract.clade(phy=tree_removedTips,node=c(194), collapse.singles = TRUE,interactive = FALSE)
outgroups<- tree_removedTips$tip.label[which(tree_removedTips$tip.label %in% core$tip.label==FALSE)]
outgroups_araneidae<-outgroups
tree_removedTips<-drop.tip(tree_removedTips,outgroups)2.2 Theridiidae phylogeny
#Load Theridiidae tree
tree_theridiidae<-read.nexus("total_Theridiidae_tree.tre")
#load fixed tip names
nam_tree<-read_delim("theridiidae_tips.txt",col_names=F)
tree_theridiidae$tip.label<-nam_tree$X2
#Remove repeated tips
tree_removed_theridiidae<-remove_duplicate_tips(tree_theridiidae)
#remove problematic tips
problematic_tips<-c("Chrysso_albipes","Chrysso_sp","Erigone_dentosa")
tree_removed_theridiidae<-drop.tip(tree_removed_theridiidae,c(problematic_tips))
#Identify the outgroup
#plotTree(tree_removed_theridiidae)
#nodelabels()
outgroups<-extract.clade(phy=tree_removed_theridiidae, node=304, root.edge = 0, collapse.singles = TRUE,interactive = FALSE) #Keep an eye on the node
outgroups_theridiidae<-outgroupsNow with the two phylogenies, we are going to join them fro further analyses
2.3 Join the phylogenies
calib<-makeChronosCalib(tree_removed_theridiidae, age.min = max(node.depth.edgelength(tree_removedTips)), age.max = max(node.depth.edgelength(tree_removedTips)))
tmp_t<-chronos(tree_removed_theridiidae, lambda = 1, model = "correlated", quiet = FALSE,
calibration = calib,
control = chronos.control())##
## Setting initial dates...
## Fitting in progress... get a first set of estimates
## (Penalised) log-lik = -628.3153
## Optimising rates... dates... -628.3153
##
## log-Lik = -628.3153
## PHIIC = 2190.63joint_trees_outgroups<-bind.tree(tree_removedTips,tmp_t, interactive = FALSE)
joint_trees<-bind.tree(tree_removedTips, ape::drop.tip(phy=tmp_t,outgroups$tip.label), interactive = FALSE)
# get scaled edge.length
joint_trees$edge.length <- joint_trees$edge.length / (max(joint_trees$edge.length))
#Remove duplicate tips
joint_trees<-remove_duplicate_tips(joint_trees)
#Check that the final tree is ultrametric
joint_trees<-check_and_fix_ultrametric(joint_trees)3 Load data and data matching
#load the csv file
join_dataset<-read_csv("data_total.csv",col_names=T)
#replace spaces in species names
join_dataset$species<-gsub(pattern=" ", replacement="_",join_dataset$species)
#keep unique rows
join_dataset<-distinct(join_dataset,species,.keep_all = TRUE)
#Tranform presence in islands to a binary variable
join_dataset<-join_dataset %>% mutate(bin_island=ifelse(cat_island=="island"|cat_island=="island_continent",1,0))
#replace spaces in species names on the tree
join_tree<-multi2di(joint_trees)
join_tree$tip.label<-gsub(pattern=" ", replacement="_",join_tree$tip.label)
##Check if the table match the tree tips
#remove species that are not in the phylogeny
join_dataset<-join_dataset[join_dataset$species %in% join_tree$tip.label,]
##Add species with no information into the phylogeny, like XX_sp
for(spe in unique(join_tree$tip.label)){
#Remove
if(spe %in% join_dataset$species==FALSE){
print(spe)
join_dataset<-join_dataset %>% add_row(species=spe)
}
}
#Let's modify the dataset to deal with colour polytipic species
join_dataset$polymorphism[which(join_dataset$polymorphism %in% c("polytipic","possible polytipic","pattern variable")==TRUE)]<-NA
join_dataset<-join_dataset %>% filter(!is.na(polymorphism))
dataset_all_species_phylogeny<-join_datasetNow we have a single and a dataset that match each other.
4 Phylogeny visualization
Let’s see how is the presence of colour polymorphism present in the phylogeny
#Change tree name
to_plot_tree<-join_tree
#Find colour polymorphic lineages
otus<-join_dataset %>% filter(polymorphism=="yes") %>% pull(species)
to_plot_tree<-groupOTU(to_plot_tree, otus)
df_polymorphism<-data.frame(join_dataset$polymorphism)
#df_island<-data.frame(as.character(join_dataset$bin_island))
rownames(df_polymorphism)<-join_dataset$species
#Plot tree with names
p<-ggtree(to_plot_tree, layout='circular') + geom_tiplab()
#pdf("total_tree_names.pdf", width=20,height=20)
#plot(p)
#dev.off()
#Plot tree colour polymorphism
p<-ggtree(to_plot_tree, layout='circular')
#pdf("total_tree_polymorphism.pdf", width=20,height=20)
gheatmap(p, df_polymorphism, offset=.001, width=.08,colnames = FALSE, colnames_offset_y = 1)+scale_fill_manual(values=c("#1ABEC6","#FF5B00"),name="Presence of\ncolour polymorphism")
#dev.off()5 Filter species with poor geographical information
Arachnids is one of the groups with the poorest geographic information available in public databases.For instance, in our data ~51% of the species has less than 50 geographical records
species_points<-join_dataset %>% drop_na(n_points)
species_geo<-nrow(species_points[species_points$n_points<50,])/nrow(species_points)*100
print(paste0(species_geo,"%"," of the species with geographical information has less than 50 geographical records"))## [1] "52.6881720430108% of the species with geographical information has less than 50 geographical records"To account for this, we decided to calculated the mean and its 95% confidence interval (CI) for the number of geographical records available for all the species. We excluded species from the subsequent analyses that fell outside the lower CI.
#Due to high vari
l_points<-na.omit(log(join_dataset$n_points))
##Let's calculate the 95% around the mean
library(boot)
data <- data.frame(xs = l_points)
bo <- boot(data[, "xs", drop = FALSE], statistic=meanfun, R=5000)
mean_ci<-boot.ci(bo, conf=0.95, type="bca")
ggplot(tibble(x=bo$t[,1]), aes(x=x)) +geom_density()+geom_segment(x=mean_ci$bca[4],xend=mean_ci$bca[5],y=0,yend=0,color="blue",size=2,lineend="round")
##Remove species with low number of records
datos_filtered<-join_dataset %>% filter(n_points>=exp(mean_ci$bca[4]))
#let's keep this filtered dataset for further analyses
data_filtered_phylogeny<-datos_filtered6 Statistical models with the remaining species
all the predictors seems skewed or not uniform distributed, let’s modify some predictors that may affect the regression due to their non-normal distribution
datos_filtered$T_centroid_lat<-abs(datos_filtered$centroid_lat)
datos_filtered$T_lat_range<-sqrt(abs(datos_filtered$lat_range))
datos_filtered$T_area_polygon<-sqrt(datos_filtered$area_polygon+1)
datos_filtered$T_lat_range_wsc<-abs(datos_filtered$lat_range_wsc)
datos_filtered$T_area_countries_wsc<-sqrt(datos_filtered$area_countries_wsc)
datos_filtered$T_points<-log(datos_filtered$n_points)
datos_filtered$T_bole<-log(datos_filtered$bole_female)6.1 Analyses total samples
Remove species from islands that can affect calculations due to their geographic limit for dispersion
datos_filtered_total<-datos_filtered %>% filter(cat_island != "island") %>% data.frame()Number of colour monomorphic and polymorphic species
table(datos_filtered_total$polymorphism)##
## no yes
## 55 33Correlation plot between the variables
cor_matrix <- cor(na.omit(datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")]))
colnames(cor_matrix)<c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSErownames(cor_matrix)<-c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
par(mfrow=c(1,1))
corrplot(cor_matrix, method = "number", type = "upper", order = "original", tl.cex=1, )
Standardize variable before the analysis, excluding the count variables
datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()Now, let’s prepare the dataset and tree so they match, this is super important. Your phylogeny names need to match a column of data
Let’s run the models!
6.1.1 Association between colour polymorphism and number of records and latitude of the centroid
Evaluate if the colour monomorphic and colour polymorphic species differ in the number of records
set.seed(30011994)
brm_points <- brm(
n_points ~ polymorphism,
data = datos_filtered_total,
family = negbinomial(),
#prior = prior,
#data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start sampling#pairs(brm_points)
summary(brm_points)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: n_points ~ polymorphism
## Data: datos_filtered_total (Number of observations: 88)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 7.09 0.18 6.76 7.45 1.00 27910 21792
## polymorphismyes 0.60 0.29 0.03 1.18 1.00 26933 22879
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 0.59 0.08 0.45 0.75 1.00 27738 24086
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Check if the predicted values fits the rawdata
#r2
r2_bayes(brm_points)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.044 (95% CI [8.179e-12, 0.169])#
pp_check(brm_points)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_points))
They do not have differences in the number of records
Evaluate if the colour monomorphic and colour polymorphic species differ in the latitude of the centroid
set.seed(30011994)
brm_centroid <- brm(
T_centroid_lat ~ polymorphism,
data = datos_filtered_total,
family = skew_normal(),
#prior = prior,
# data2 = list(A = A),
control = list(adapt_delta = 0.99999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start sampling#pairs(brm_centroid)
summary(brm_centroid)## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_centroid_lat ~ polymorphism
## Data: datos_filtered_total (Number of observations: 88)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.12 0.13 -0.15 0.38 1.00 24113 22217
## polymorphismyes -0.29 0.21 -0.70 0.11 1.00 27030 23861
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.03 0.09 0.88 1.22 1.00 21950 22086
## alpha -2.32 1.79 -5.72 1.06 1.00 18719 23412
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_centroid)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.020 (95% CI [1.869e-10, 0.088])## Check if the predicted values fits the rawdata
pp_check(brm_centroid)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_centroid))
They do not have differences in the latitude of the centroid
Evaluate if the colour monomorphic and colour polymorphic species differ in the body length
set.seed(30011994)
brm_bole <- brm(
T_bole ~ polymorphism,
data = datos_filtered_total,
family = gaussian(),
#prior = prior,
#data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(brm_bole)
summary(brm_bole)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: T_bole ~ polymorphism
## Data: datos_filtered_total (Number of observations: 87)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.12 0.14 -0.39 0.16 1.00 28896 23382
## polymorphismyes 0.31 0.22 -0.13 0.74 1.00 26593 23574
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.01 0.08 0.87 1.18 1.00 26318 22367
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Check if the predicted values fits the rawdata
#r2
r2_bayes(brm_bole)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.022 (95% CI [3.928e-11, 0.096])pp_check(brm_bole)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_bole))
They do not have differences in body length
let’s Evaluate the association fo the predictors
lm_lat_range <- lm(T_lat_range ~ polymorphism+T_bole+T_centroid_lat, data=datos_filtered_total)
check_collinearity(lm_lat_range)The predictors are not collinear, we can use all of them in the models
6.1.2 Latitudinal range
set.seed(30011994)
brm_latrange_1 <- brm(
T_lat_range ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = datos_filtered_total,
family = skew_normal(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start sampling## Warning: There were 3 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.## Warning: There were 3203 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded## Warning: Examine the pairs() plot to diagnose sampling problemspairs(brm_latrange_1)
summary(brm_latrange_1)## Warning: There were 3 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_lat_range ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: datos_filtered_total (Number of observations: 87)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 87)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.55 0.30 0.04 1.13 1.00 1990 2895
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.12 0.24 -0.59 0.37 1.00 19120 13780
## polymorphismyes 0.48 0.23 0.03 0.94 1.00 15277 24382
## T_bole 0.14 0.13 -0.12 0.40 1.00 27487 26101
## T_centroid_lat -0.37 0.14 -0.62 -0.10 1.00 25448 29758
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.79 0.14 0.47 1.03 1.00 2249 2410
## alpha 0.68 2.59 -4.56 6.37 1.00 9071 10600
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Check if the predicted values fits the rawdata
#r2
r2_bayes(brm_latrange_1)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.407 (95% CI [0.134, 0.763])
## Marginal R2: 0.280 (95% CI [0.106, 0.434])pp_check(brm_latrange_1)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_latrange_1))
6.1.3 Range size calculated with the area of the Convex polygon
area_polygon_1 <- brm(
T_area_polygon ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)),
data = datos_filtered_total,
family = skew_normal(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(area_polygon_1)
summary(area_polygon_1)## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_area_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: datos_filtered_total (Number of observations: 86)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 86)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.25 0.17 0.01 0.63 1.00 7630 14681
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.05 0.17 -0.38 0.30 1.00 28839 24956
## polymorphismyes 0.30 0.21 -0.12 0.72 1.00 37396 28560
## T_bole 0.12 0.12 -0.11 0.36 1.00 34910 28757
## T_centroid_lat 0.12 0.13 -0.13 0.37 1.00 37907 28881
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.96 0.09 0.80 1.15 1.00 23827 24049
## alpha 3.56 1.53 1.38 7.41 1.00 20099 16445
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Check if the predicted values fits the rawdata
#r2
r2_bayes(area_polygon_1)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.104 (95% CI [0.005, 0.253])
## Marginal R2: 0.061 (95% CI [9.604e-04, 0.155])pp_check(area_polygon_1)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(area_polygon_1))
6.1.4 Ecological regions
To indirectly explore the difference in niche width between colour monomorphic and polymorphic species, we measured the number of ecological regions occupy by each species using the geographical records and polygons. the ecological regions were obtained here
BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on geographical records
set.seed(30011994)
eco_reg_points_1 <- brm(
eco_reg_points ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = datos_filtered_total,
family = poisson(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(eco_reg_points_1)
summary(eco_reg_points_1)## Family: poisson
## Links: mu = log
## Formula: eco_reg_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: datos_filtered_total (Number of observations: 87)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 87)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.25 0.12 1.04 1.51 1.00 7540 14794
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.08 0.40 2.29 3.87 1.00 5039 10352
## polymorphismyes 0.40 0.21 -0.02 0.82 1.00 5591 11226
## T_bole 0.27 0.14 -0.02 0.55 1.00 6300 11905
## T_centroid_lat 0.11 0.12 -0.11 0.34 1.00 6339 12525
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Check if the predicted values fits the rawdata
#r2
r2_bayes(eco_reg_points_1)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.964 (95% CI [0.948, 0.978])
## Marginal R2: 0.108 (95% CI [4.214e-04, 0.389])pp_check(eco_reg_points_1)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(eco_reg_points_1))
BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on polygon
eco_reg_polygon_1 <- brm(
eco_reg_polygon~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = datos_filtered_total,
family = poisson(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(eco_reg_polygon_1)
summary(eco_reg_polygon_1)## Family: poisson
## Links: mu = log
## Formula: eco_reg_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: datos_filtered_total (Number of observations: 86)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 86)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.34 0.12 1.13 1.60 1.00 5866 9389
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.73 0.42 2.90 4.56 1.00 5065 9428
## polymorphismyes 0.43 0.22 -0.01 0.87 1.00 4410 8374
## T_bole 0.34 0.15 0.04 0.62 1.00 5452 9473
## T_centroid_lat -0.20 0.12 -0.44 0.05 1.00 4576 8644
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(eco_reg_polygon_1)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.985 (95% CI [0.978, 0.991])
## Marginal R2: 0.211 (95% CI [0.014, 0.500])## Check if the predicted values fits the rawdata
pp_check(eco_reg_polygon_1)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(eco_reg_polygon_1))
6.1.5 Climatic zones
Addtionally, we also explored if colour monomorphic and polymorphic species differ in the number of climatic zones they occupy. We measured the number of climatic zones for each species using the geographical records and polygons. the Köppen-Geiger climate classification zones were obtained here
temp_zones_points_1 <- brm(
temp_zones_points~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = datos_filtered_total,
family = negbinomial(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(temp_zones_points_1)
summary(temp_zones_points_1)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: temp_zones_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: datos_filtered_total (Number of observations: 87)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 87)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.11 0.08 0.00 0.29 1.00 9200 16498
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.04 0.07 1.88 2.18 1.00 29056 21791
## polymorphismyes 0.16 0.09 -0.02 0.35 1.00 45883 28344
## T_bole 0.19 0.05 0.09 0.29 1.00 41828 30021
## T_centroid_lat 0.09 0.05 -0.00 0.19 1.00 44202 29165
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 56.13 52.35 12.70 203.40 1.00 32992 29077
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(temp_zones_points_1)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.268 (95% CI [0.106, 0.453])
## Marginal R2: 0.224 (95% CI [0.075, 0.385])## Check if the predicted values fits the rawdata
pp_check(temp_zones_points_1)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(temp_zones_points_1))
temp_zones_polygon_1 <- brm(
temp_zones_polygon~polymorphism+T_bole+T_centroid_lat+ (1| gr(species, cov = A)) ,
data = datos_filtered_total,
family = negbinomial(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(temp_zones_polygon_1)
summary(temp_zones_polygon_1)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: temp_zones_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: datos_filtered_total (Number of observations: 86)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 86)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.08 0.07 0.00 0.24 1.00 15301 19325
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.55 0.07 2.40 2.69 1.00 40759 27503
## polymorphismyes -0.00 0.10 -0.20 0.20 1.00 57512 29246
## T_bole 0.03 0.06 -0.09 0.13 1.00 49899 30684
## T_centroid_lat -0.18 0.06 -0.29 -0.07 1.00 53189 30435
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 9.47 3.28 5.14 17.50 1.00 48501 23980
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(temp_zones_polygon_1)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.243 (95% CI [0.091, 0.396])
## Marginal R2: 0.207 (95% CI [0.060, 0.359])## Check if the predicted values fits the rawdata
pp_check(temp_zones_polygon_1)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(temp_zones_polygon_1))
all_models<-NULL
for(mod in c("brm_latrange_1","area_polygon_1","eco_reg_points_1","eco_reg_polygon_1","temp_zones_polygon_1","temp_zones_points_1")){
baye_mode = get(mod)
bayes_results<-baye_mode %>%
spread_draws(b_polymorphismyes)
bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
all_models<-bind_rows(all_models, bayes_results)
}
all_models %>% ggplot(aes(y = model, x = b_polymorphismyes)) +
stat_halfeye()+
theme_classic()+
geom_vline(xintercept = 0, linetype = "dashed",col="black",size=1)+
labs(x="Estimate",y="Models")
Plot of the model
paleta1<-c("#1ABEC6","#FF5B00")
dataset_plot<-datos_filtered_total %>% drop_na(T_lat_range|polymorphism|T_bole|T_centroid_lat)
dataset_plot$predict<-predict(brm_latrange_1,type="response")[,"Estimate"]
dataset_plot %>% ggplot(aes(x=polymorphism,y=predict,fill=polymorphism))+geom_point(aes(x=polymorphism,y=T_lat_range),shape = 21,size=3, position = position_jitterdodge(),alpha=0.5)+geom_violin(aes(x=polymorphism,y=T_lat_range),alpha=0.1, position = position_dodge(width = .75),size=1)+
stat_summary(fun = mean,aes(color = polymorphism,group=polymorphism),fun.min = function(x) mean(x) - (2*se(x)),fun.max = function(x) mean(x)+(2*se(x)),geom = "pointrange",shape=22,size=1.5,col="black")+scale_fill_manual(values=paleta1)+scale_colour_manual(values=paleta1)+theme_classic()+labs(x="Colour polymorphism",y="Latitudinal range")
6.2 Predictive confidence interval
To eliminate any false association caused by sampling bias, we repeated the above analyses with a reduced dataset. The subset was created by calculating a linear regression between the number of geographical records and the geographical area of the regions described in the WSC (a positive relationship), and then discarding species outside the lower boundary of the 50% predictive confidence interval (Quantile 0.75 and Quantile 0.25). In this way we only kept species with a small number of records when their WSC calculated range was calculated as very small (Predictive interval subset; supplementary figure 2). This approach is different from using a threshold for the number of points because it acknowledges that some species will have fewer records if their range is very restricted.
Let’s generate the dataset
no_island<-datos_filtered %>% filter(cat_island!="island") %>% drop_na(n_points) %>% drop_na(area_polygon) %>%drop_na(polymorphism)
no_island<-na.omit(no_island)
no_island[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(no_island[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()
lm_points<-lm(T_points~T_area_countries_wsc,data=no_island)
summary(lm_points)##
## Call:
## lm(formula = T_points ~ T_area_countries_wsc, data = no_island)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3549 -0.5525 -0.0333 0.5903 1.7387
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.694e+00 3.466e-01 -4.889 5.73e-06 ***
## T_area_countries_wsc 3.289e-04 6.445e-05 5.103 2.50e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8659 on 74 degrees of freedom
## Multiple R-squared: 0.2603, Adjusted R-squared: 0.2503
## F-statistic: 26.04 on 1 and 74 DF, p-value: 2.503e-06no_island<-cbind(no_island,predict(lm_points,interval="prediction",level=0.50))## this plots the q10% and q90%## Warning in predict.lm(lm_points, interval = "prediction", level = 0.5): predictions on current data refer to _future_ responsesggplot(no_island,aes(T_area_countries_wsc,T_points))+geom_point(size=3,aes(col=polymorphism))+ geom_smooth(method = "lm",level=0.99)+geom_line(aes(y=upr),col="red")+geom_line(aes(y=lwr),col="red")+theme_bw()## `geom_smooth()` using formula = 'y ~ x'
##subset based on the prediction intervals
pi_subset<-no_island[!no_island$T_points<no_island$lwr,]Number of colour monomorphic and polymorphic species after filtering
table(pi_subset$polymorphism)##
## no yes
## 35 24Correlation plot between the variables
cor_matrix <- cor(na.omit(pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")]))
colnames(cor_matrix)<c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSErownames(cor_matrix)<-c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
par(mfrow=c(1,1))
corrplot(cor_matrix, method = "number", type = "upper", order = "original", tl.cex=1, )
Standardize variable before the analysis, excluding the count variables
pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()Now, let’s prepare the dataset and tree so they match, this is super important. Your phylogeny names need to match a column of data
Let’s run the models!
6.2.1 Association between colour polymorphism and number of records and latitude of the centroid
Evaluate if the colour monomorphic and colour polymorphic species differ in the number of records
set.seed(30011994)
brm_points <- brm(
n_points ~ polymorphism,
data = pi_subset,
family = negbinomial(),
#prior = prior,
#data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(brm_points)
summary(brm_points)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: n_points ~ polymorphism
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 7.45 0.19 7.11 7.83 1.00 28973 20786
## polymorphismyes 0.54 0.29 -0.01 1.12 1.00 28206 23883
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 0.88 0.14 0.62 1.19 1.00 29632 24685
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_points)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.061 (95% CI [6.155e-11, 0.222])## Check if the predicted values fits the rawdata
pp_check(brm_points)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_points))
They do not have differences in the number of records
Evaluate if the colour monomorphic and colour polymorphic species differ in the latitude of the centroid
set.seed(30011994)
brm_centroid <- brm(
T_centroid_lat ~ polymorphism,
data = pi_subset,
family = skew_normal(),
#prior = prior,
#data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(brm_centroid)
summary(brm_centroid)## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_centroid_lat ~ polymorphism
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.09 0.16 -0.24 0.41 1.00 22797 22128
## polymorphismyes -0.27 0.23 -0.72 0.20 1.00 25547 22832
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.02 0.10 0.84 1.24 1.00 20063 23658
## alpha -3.41 1.45 -6.35 -0.25 1.00 19819 14704
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Check if the predicted values fits the rawdata
pp_check(brm_centroid)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_centroid))
They do not have differences in the latitude of the centroid
Evaluate if the colour monomorphic and colour polymorphic species differ in the body length
set.seed(30011994)
brm_bole <- brm(
T_bole ~ polymorphism,
data = pi_subset,
family = gaussian(),
#prior = prior,
#data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(brm_bole)
summary(brm_bole)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: T_bole ~ polymorphism
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.15 0.17 -0.48 0.19 1.00 28787 22201
## polymorphismyes 0.36 0.27 -0.18 0.89 1.00 28785 22891
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.01 0.10 0.84 1.23 1.00 26065 22510
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_bole)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.032 (95% CI [3.796e-11, 0.135])## Check if the predicted values fits the rawdata
pp_check(brm_bole)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_bole))
They do not have differences in body length
let’s Evaluate the association fo the predictors
lm_lat_range <- lm(T_lat_range ~ polymorphism+T_bole+T_centroid_lat, data=pi_subset)
check_collinearity(lm_lat_range)The predictors are not collinear, we can use all of them in the models
6.2.2 Latitudinal range
set.seed(30011994)
brm_latrange_2 <- brm(
T_lat_range ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = pi_subset,
family = student(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start sampling## Warning: There were 1 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.## Warning: There were 2 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See
## https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded## Warning: Examine the pairs() plot to diagnose sampling problemspairs(brm_latrange_2)
summary(brm_latrange_2)## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Family: student
## Links: mu = identity; sigma = identity; nu = identity
## Formula: T_lat_range ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 59)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.44 0.32 0.02 1.13 1.00 1987 2272
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.11 0.23 -0.59 0.35 1.00 14523 8179
## polymorphismyes 0.27 0.24 -0.21 0.75 1.00 30291 25005
## T_bole 0.14 0.14 -0.14 0.42 1.00 27732 24474
## T_centroid_lat -0.47 0.15 -0.76 -0.15 1.00 15204 19601
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.69 0.16 0.32 0.95 1.00 2288 1954
## nu 20.18 14.10 2.88 55.95 1.00 31207 15943
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_latrange_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.425 (95% CI [0.165, 0.871])
## Marginal R2: 0.345 (95% CI [0.149, 0.514])## Check if the predicted values fits the rawdata
pp_check(brm_latrange_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_latrange_2))
6.2.3 Range size calculated with the area of the Convex polygon
area_polygon_2 <- brm(
T_area_polygon ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)),
data = pi_subset,
family = skew_normal(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start sampling## Warning: There were 6 divergent transitions after warmup. See
## https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## to find out why this is a problem and how to eliminate them.## Warning: Examine the pairs() plot to diagnose sampling problemspairs(area_polygon_2)
summary(area_polygon_2)## Warning: There were 6 divergent transitions after warmup. Increasing
## adapt_delta above 0.999 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_area_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 59)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.43 0.26 0.02 1.00 1.00 4202 5536
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.07 0.24 -0.60 0.38 1.00 17120 13487
## polymorphismyes 0.15 0.27 -0.36 0.69 1.00 24817 25797
## T_bole 0.18 0.15 -0.12 0.49 1.00 29630 26914
## T_centroid_lat 0.04 0.17 -0.30 0.38 1.00 24193 24204
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.89 0.14 0.61 1.16 1.00 5784 4887
## alpha 3.67 2.32 -0.72 8.95 1.00 17453 20011
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(area_polygon_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.203 (95% CI [0.007, 0.534])
## Marginal R2: 0.078 (95% CI [1.580e-04, 0.217])## Check if the predicted values fits the rawdata
pp_check(area_polygon_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(area_polygon_2))
6.2.4 Ecological regions
To indirectly explore the difference in niche width between colour monomorphic and polymorphic species, we measured the number of ecological regions occupy by each species using the geographical records and polygons. the ecological regions were obtained here
BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on geographical records
set.seed(30011994)
eco_reg_points_2 <- brm(
eco_reg_points ~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = pi_subset,
family = poisson(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(eco_reg_points_2)
summary(eco_reg_points_2)## Family: poisson
## Links: mu = log
## Formula: eco_reg_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 59)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.92 0.10 0.74 1.15 1.00 8706 15074
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.27 0.32 2.64 3.89 1.00 6454 11419
## polymorphismyes 0.31 0.19 -0.06 0.69 1.00 7169 12496
## T_bole 0.32 0.13 0.06 0.57 1.00 7817 14060
## T_centroid_lat -0.01 0.12 -0.23 0.22 1.00 7541 13820
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(eco_reg_points_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.966 (95% CI [0.946, 0.980])
## Marginal R2: 0.168 (95% CI [0.005, 0.446])## Check if the predicted values fits the rawdata
pp_check(eco_reg_points_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(eco_reg_points_2))
BRMS model exploring differences in the ecological regions occupy by monomorphic and polymorphic species based on polygon
eco_reg_polygon_2 <- brm(
eco_reg_polygon~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = pi_subset,
family = poisson(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(eco_reg_polygon_2)
summary(eco_reg_polygon_2)## Family: poisson
## Links: mu = log
## Formula: eco_reg_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 59)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.04 0.11 0.85 1.29 1.00 7426 13039
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.83 0.34 3.15 4.51 1.00 6848 11828
## polymorphismyes 0.31 0.20 -0.08 0.71 1.00 6301 11823
## T_bole 0.25 0.14 -0.03 0.53 1.00 6641 12844
## T_centroid_lat -0.10 0.13 -0.34 0.15 1.00 7012 12040
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(eco_reg_polygon_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.981 (95% CI [0.971, 0.989])
## Marginal R2: 0.147 (95% CI [0.002, 0.442])## Check if the predicted values fits the rawdata
pp_check(eco_reg_polygon_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(eco_reg_polygon_2))
6.2.5 Climatic zones
Addtionally, we also explored if colour monomorphic and polymorphic species differ in the number of climatic zones they occupy. We measured the number of climatic zones for each species using the geographical records and polygons. the Köppen-Geiger climate classification zones were obtained here
temp_zones_points_2 <- brm(
temp_zones_points~ polymorphism+T_bole+T_centroid_lat + (1| gr(species, cov = A)) ,
data = pi_subset,
family = negbinomial(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(temp_zones_points_2)
summary(temp_zones_points_2)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: temp_zones_points ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 59)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.08 0.06 0.00 0.21 1.00 16735 19833
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.19 0.07 2.04 2.32 1.00 47808 30419
## polymorphismyes 0.09 0.10 -0.10 0.28 1.00 62219 29971
## T_bole 0.19 0.05 0.08 0.30 1.00 52878 33056
## T_centroid_lat 0.06 0.05 -0.04 0.17 1.00 56526 32125
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 111.86 81.14 24.88 326.68 1.00 70427 31841
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(temp_zones_points_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.370 (95% CI [0.168, 0.553])
## Marginal R2: 0.330 (95% CI [0.117, 0.503])## Check if the predicted values fits the rawdata
pp_check(temp_zones_points_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(temp_zones_points_2))
temp_zones_polygon_2 <- brm(
temp_zones_polygon~polymorphism+T_bole+T_centroid_lat+ (1| gr(species, cov = A)) ,
data = pi_subset,
family = negbinomial(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 20000
)## Compiling Stan program...## Start samplingpairs(temp_zones_polygon_2)
summary(temp_zones_polygon_2)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: temp_zones_polygon ~ polymorphism + T_bole + T_centroid_lat + (1 | gr(species, cov = A))
## Data: pi_subset (Number of observations: 59)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 59)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.12 0.09 0.00 0.34 1.00 10169 14541
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.59 0.09 2.40 2.77 1.00 34947 24169
## polymorphismyes -0.07 0.12 -0.32 0.17 1.00 50435 29395
## T_bole 0.00 0.07 -0.13 0.14 1.00 37937 28154
## T_centroid_lat -0.24 0.07 -0.38 -0.11 1.00 45371 30099
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 11.34 8.38 4.69 28.19 1.00 23041 15203
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(temp_zones_polygon_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.383 (95% CI [0.172, 0.557])
## Marginal R2: 0.323 (95% CI [0.116, 0.510])## Check if the predicted values fits the rawdata
pp_check(temp_zones_polygon_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(temp_zones_polygon_2))
all_models<-NULL
for(mod in c("brm_latrange_2","area_polygon_2","eco_reg_points_2","eco_reg_polygon_2","temp_zones_polygon_2","temp_zones_points_2")){
baye_mode = get(mod)
bayes_results<-baye_mode %>%
spread_draws(b_polymorphismyes)
bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
all_models<-bind_rows(all_models, bayes_results)
}
all_models %>% ggplot(aes(y = model, x = b_polymorphismyes)) +
stat_halfeye()+
theme_classic()+
geom_vline(xintercept = 0, linetype = "dashed",col="black",size=1)+
labs(x="Estimate",y="Models")
Plot of the model
paleta1<-c("#1ABEC6","#FF5B00")
dataset_plot<-pi_subset %>% drop_na(T_lat_range|polymorphism|T_bole|T_centroid_lat)
dataset_plot$predict<-predict(brm_latrange_2,type="response")[,"Estimate"]
dataset_plot %>% ggplot(aes(x=polymorphism,y=predict,fill=polymorphism))+geom_point(aes(x=polymorphism,y=T_lat_range),shape = 21,size=3, position = position_jitterdodge(),alpha=0.5)+geom_violin(aes(x=polymorphism,y=T_lat_range),alpha=0.1, position = position_dodge(width = .75),size=1)+
stat_summary(fun = mean,aes(color = polymorphism,group=polymorphism),fun.min = function(x) mean(x) - (2*se(x)),fun.max = function(x) mean(x)+(2*se(x)),geom = "pointrange",shape=22,size=1.5,col="black")+scale_fill_manual(values=paleta1)+scale_colour_manual(values=paleta1)+theme_classic()+labs(x="Colour polymorphism",y="Latitudinal range")
7 models without considering the phylogeny
We observed that the models with continous variables have values close to 0 and that the climatic zones models have random effects low variaces close to 0. This means that the phylogentic relationships of the individuals are not having a major effect on these models.
hyp <- "sd_species__Intercept^2 / (sd_species__Intercept^2 + sigma^2) = 0"
lat_range_sig <- hypothesis(brm_latrange_1, hyp, class = NULL)
area_sig<-hypothesis(area_polygon_1, hyp, class = NULL)
ggplot() + geom_histogram(aes(x = lat_range_sig$samples$H1, fill="Latitudinal range model"), alpha = 0.5)+
geom_histogram(aes(x = area_sig$samples$H1,fill="Area polygon model"), alpha = 0.5)+labs(x="Pagel's lambda",y="Count")+theme_classic()## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
In consequence, we decided to run a set of models without considering the phylogeny. This let us include more species with good geographic records but that were not include in the phylogenetic reconstruction due to lack of genetic data.
7.1 Reload data
join_dataset<-read_csv("data_total.csv",col_names=T)
join_dataset$species<-gsub(pattern=" ", replacement="_",join_dataset$species)
#keep unique rows
join_dataset<-distinct(join_dataset,species,.keep_all = TRUE)
###Tranform island as binary
join_dataset<-join_dataset %>% mutate(bin_island=ifelse(cat_island=="island"|cat_island=="island_continent",1,0))
#Let's modify the dataset to deal with polytipic
join_dataset$polymorphism[which(join_dataset$polymorphism %in% c("polytipic","possible polytipic","pattern variable")==TRUE)]<-NA7.2 Filter species with poor geographical information
Arachnids is one of the groups with the poorest geographic information available in public databases. For instance, in our data ~52% of the species has less than 50 geographical records
species_points<-join_dataset %>% drop_na(n_points)
species_geo<-nrow(species_points[species_points$n_points<50,])/nrow(species_points)*100
print(paste0(species_geo,"%"," of the species with geographical information has less than 50 geographical records"))## [1] "52.0179372197309% of the species with geographical information has less than 50 geographical records"To account for this, we decided to calculated the mean and its 95% confidence interval (CI) for the number of geographical records available for all the species. We excluded species from the subsequent analyses that fell outside the lower CI.
#Due to high vari
l_points<-na.omit(log(join_dataset$n_points))
##Let's calculate the 95% around the mean
library(boot)
data <- data.frame(xs = l_points)
bo <- boot(data[, "xs", drop = FALSE], statistic=meanfun, R=5000)
mean_ci<-boot.ci(bo, conf=0.95, type="bca")
ggplot(tibble(x=bo$t[,1]), aes(x=x)) +geom_density()+geom_segment(x=mean_ci$bca[4],xend=mean_ci$bca[5],y=0,yend=0,color="blue",size=2,lineend="round")
##Remove species with low number of records
datos_filtered<-join_dataset %>% filter(n_points>=exp(mean_ci$bca[4]))
#datos_filtered<-na.omit(datos_filtered)
##Let's save this dataset for further analyses
data_without_filtering<-datos_filteredall the predictors seems skewed or not uniform distributed, let’s modify some predictors that may affect the regression due to their non-normal distribution
datos_filtered$T_centroid_lat<-abs(datos_filtered$centroid_lat)
datos_filtered$T_lat_range<-sqrt(abs(datos_filtered$lat_range))
datos_filtered$T_area_polygon<-sqrt(datos_filtered$area_polygon+1)
datos_filtered$T_lat_range_wsc<-abs(datos_filtered$lat_range_wsc)
datos_filtered$T_area_countries_wsc<-sqrt(datos_filtered$area_countries_wsc)
datos_filtered$T_points<-log(datos_filtered$n_points)
datos_filtered$T_bole<-log(datos_filtered$bole_female)Correlation plot between the variables
cor_matrix <- cor(na.omit(pi_subset[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")]))
colnames(cor_matrix)<c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")## [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSErownames(cor_matrix)<-c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon","eco_reg_points","eco_reg_polygon","temp_zones_points","temp_zones_polygon")
par(mfrow=c(1,1))
corrplot(cor_matrix, method = "number", type = "upper", order = "original", tl.cex=1, )
7.3 Analyses
Remove species from islands that can affect calculations due to their geographic limit for dispersion
datos_filtered_total<-datos_filtered %>% filter(cat_island != "island") %>% data.frame()Standardize variable before the analysis, excluding the count variables
datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]<-standard_varibles(datos_filtered_total[,c("T_points","T_centroid_lat","T_bole","T_lat_range","T_area_polygon")]) %>% data.frame()Number of colour monomorphic and polymorphic species
table(datos_filtered_total$polymorphism)##
## no yes
## 53 41Let’s run the models!
7.3.1 Association between colour polymorphism and the latitude of the centroid
Evaluate if the colour monomorphic and colour polymorphic species differ in the latitude of the centroid
set.seed(30011994)
brm_centroid <- brm(
T_centroid_lat ~ polymorphism,
data = datos_filtered_total,
family = skew_normal(),
#prior = prior,
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(brm_centroid)
summary(brm_centroid)## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_centroid_lat ~ polymorphism
## Data: datos_filtered_total (Number of observations: 94)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.24 0.14 -0.03 0.51 1.00 27520 24269
## polymorphismyes -0.48 0.21 -0.89 -0.09 1.00 27572 26365
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.01 0.08 0.87 1.19 1.00 22513 22267
## alpha -0.69 1.89 -4.79 2.76 1.00 17619 18114
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_centroid)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.058 (95% CI [5.563e-11, 0.148])## Check if the predicted values fits the rawdata
pp_check(brm_centroid)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_centroid))
They do not have differences in the latitude of the centroid
Evaluate if the colour monomorphic and colour polymorphic species differ in the body length
set.seed(30011994)
brm_bole <- brm(
T_bole ~ polymorphism,
data = datos_filtered_total,
family = gaussian(),
#prior = prior,
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(brm_bole)
summary(brm_bole)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: T_bole ~ polymorphism
## Data: datos_filtered_total (Number of observations: 93)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.14 0.14 -0.42 0.13 1.00 28008 23443
## polymorphismyes 0.29 0.21 -0.12 0.69 1.00 28086 23611
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.99 0.07 0.85 1.14 1.00 26984 23947
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_bole)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.022 (95% CI [1.708e-10, 0.093])## Check if the predicted values fits the rawdata
pp_check(brm_bole)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_bole))
They do not have differences in their body length
let’s Evaluate the association fo the predictors
lm_lat_range <- lm(T_lat_range ~ polymorphism+T_bole+T_centroid_lat, data=datos_filtered_total)
check_collinearity(lm_lat_range)The predictors are not collinear, we can use all of them in the models
7.3.2 Latitudinal range
set.seed(30011994)
brm_latrange_3 <- brm(
T_lat_range ~ polymorphism+T_bole+T_centroid_lat,
data = datos_filtered_total,
family = gaussian(),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(brm_latrange_3)
summary(brm_latrange_3)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: T_lat_range ~ polymorphism + T_bole + T_centroid_lat
## Data: datos_filtered_total (Number of observations: 93)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.13 0.12 -0.37 0.12 1.00 31410 26476
## polymorphismyes 0.21 0.19 -0.17 0.58 1.00 31518 28245
## T_bole 0.16 0.10 -0.04 0.35 1.00 30238 28406
## T_centroid_lat -0.29 0.10 -0.49 -0.09 1.00 28182 27399
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.87 0.07 0.75 1.01 1.00 30294 26578
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_latrange_3)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.211 (95% CI [0.087, 0.332])## Check if the predicted values fits the rawdata
pp_check(brm_latrange_3)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(brm_latrange_3))
7.3.3 Range size calculated with the area of the Convex polygon
area_polygon_3 <- brm(
T_area_polygon ~ polymorphism+T_bole+T_centroid_lat,
data =datos_filtered_total,
family = skew_normal(),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(area_polygon_3)
summary(area_polygon_3)## Family: skew_normal
## Links: mu = identity; sigma = identity; alpha = identity
## Formula: T_area_polygon ~ polymorphism + T_bole + T_centroid_lat
## Data: datos_filtered_total (Number of observations: 92)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.06 0.13 -0.32 0.21 1.00 24474 25412
## polymorphismyes 0.15 0.19 -0.21 0.54 1.00 26437 25469
## T_bole 0.14 0.10 -0.07 0.34 1.00 25404 25232
## T_centroid_lat 0.10 0.11 -0.11 0.32 1.00 23426 25751
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.98 0.08 0.83 1.15 1.00 21237 23137
## alpha 3.46 1.27 1.50 6.52 1.00 19734 14825
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(area_polygon_3)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.041 (95% CI [3.590e-04, 0.115])## Check if the predicted values fits the rawdata
pp_check(area_polygon_3)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
plot(conditional_effects(area_polygon_3))
7.3.4 Climatic zones
Addtionally, we also explored if colour monomorphic and polymorphic species differ in the number of climatic zones they occupy. We measured the number of climatic zones for each species using the geographical records and polygons. the Köppen-Geiger climate classification zones were obtained here
temp_zones_points_3 <- brm(
temp_zones_points~ polymorphism+T_bole+T_centroid_lat ,
data = datos_filtered_total,
family = negbinomial(),
#prior = prior,
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 10000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(temp_zones_points_3)
summary(temp_zones_points_3)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: temp_zones_points ~ polymorphism + T_bole + T_centroid_lat
## Data: datos_filtered_total (Number of observations: 93)
## Draws: 4 chains, each with iter = 10000; warmup = 5000; thin = 1;
## total post-warmup draws = 20000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.06 0.06 1.94 2.17 1.00 16363 13437
## polymorphismyes 0.11 0.08 -0.06 0.28 1.00 16701 14119
## T_bole 0.19 0.05 0.10 0.28 1.00 14180 12832
## T_centroid_lat 0.10 0.04 0.01 0.19 1.00 14939 13747
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 42.09 39.27 11.28 150.32 1.00 13361 10787
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(temp_zones_points_3)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.201 (95% CI [0.068, 0.333])## Check if the predicted values fits the rawdata
pp_check(temp_zones_points_3)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
#plot(conditional_effects(temp_zones_points))temp_zones_polygon_3 <- brm(
temp_zones_polygon~polymorphism+T_bole+T_centroid_lat ,
data = datos_filtered_total,
family = negbinomial(),
#prior = prior,
control = list(adapt_delta = 0.999, max_treedepth=20)
,chains = 4, cores = 4, iter = 10000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(temp_zones_polygon_3)
summary(temp_zones_polygon_3)## Family: negbinomial
## Links: mu = log; shape = identity
## Formula: temp_zones_polygon ~ polymorphism + T_bole + T_centroid_lat
## Data: datos_filtered_total (Number of observations: 92)
## Draws: 4 chains, each with iter = 10000; warmup = 5000; thin = 1;
## total post-warmup draws = 20000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.59 0.06 2.46 2.71 1.00 18249 13635
## polymorphismyes -0.04 0.10 -0.24 0.15 1.00 17091 13537
## T_bole 0.05 0.05 -0.05 0.15 1.00 15940 13481
## T_centroid_lat -0.17 0.05 -0.28 -0.06 1.00 14470 12866
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape 8.22 2.32 4.80 13.73 1.00 17084 13504
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(temp_zones_polygon_3)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.196 (95% CI [0.065, 0.332])## Check if the predicted values fits the rawdata
pp_check(temp_zones_polygon_3)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
#plot(conditional_effects(temp_zones_polygon))7.3.5 Summary of the models
all_models<-NULL
for(mod in c("brm_latrange_3","area_polygon_3","temp_zones_polygon_3","temp_zones_points_3")){
baye_mode = get(mod)
bayes_results<-baye_mode %>%
spread_draws(b_polymorphismyes)
bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
all_models<-bind_rows(all_models, bayes_results)
}
all_models %>% ggplot(aes(y = model, x = b_polymorphismyes)) +
stat_halfeye()+
theme_classic()+
geom_vline(xintercept = 0, linetype = "dashed",col="black",size=1)+
labs(x="Estimate",y="Models")
8 Island models
Considering that the presence on islands can be an indicator of range expansion, we also recorded whether species were distributed on islands by overlapping both sources of geographical distribution (occurrences and WSC) with the global shoreline vector from the islands database (Sayre et al., 2019).
We decided to test the association between colour polymorphism and the presence on islands using two datasets. The first one was using the species occurrences after discarding those species with poor geographic records as done here
##Remove species with low number of records
data_filtered_phylogeny<-data_filtered_phylogeny %>% drop_na(polymorphism) %>% drop_na(bin_island)
table(data_filtered_phylogeny$polymorphism)##
## no yes
## 56 35This dataset includes 56 colour monomorphic species and 35 colour polymorphic species.
To increase the number of species in our analysis, we created a second dataset without filtering species based on the number of geographic records. We determined the presence on islands using the geographic distribution information available on the World Spider Catalog.
dataset_all_species_phylogeny<-dataset_all_species_phylogeny %>% drop_na(n_points) %>%drop_na(polymorphism) %>% drop_na(bin_island) %>% drop_na(cat_island_points)
table(dataset_all_species_phylogeny$polymorphism)##
## no yes
## 125 61This second dataset includes 125 colour monomorphic species and 61 colour polymorphic species.
8.1 Presence on island using filtered dataset
## Family: bernoulli
## Links: mu = logit
## Formula: bin_island ~ 1 + polymorphism + log(bole_female) + (1 | gr(species, cov = A))
## Data: data_filtered_phylogeny (Number of observations: 90)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 90)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 3.95 4.27 0.27 13.24 1.00 4645 5970
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.34 4.36 -3.61 12.40 1.00 16517 9781
## polymorphismyes 4.82 3.61 1.11 13.50 1.00 8832 6606
## logbole_female -0.13 1.70 -3.01 3.21 1.00 17294 12729
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.466 (95% CI [0.064, 0.853])
## Marginal R2: 0.023 (95% CI [0.000, 0.252])
With this dataset there seems to be an association between
colour polymorphism and the presence on islands
## .
## 0 1
## 0.2142857 0.7857143## .
## 0 1
## 0.02857143 0.97142857
8.2 Presence on island using most of the species in phylogeny
tree=check_and_fix_ultrametric(join_tree)
missing<-tree$tip.label[which(tree$tip.label %in% dataset_all_species_phylogeny$species==FALSE)]
island_dataset_tree<-drop.tip(tree,missing)
island_dataset_tree$edge.length <- island_dataset_tree$edge.length / (max(island_dataset_tree$edge.length))
A <- ape::vcv(island_dataset_tree,corr = TRUE)
set.seed(30011994)
brm_island_2 <- brm(
bin_island ~ 1 + polymorphism + log(bole_female) + (1| gr(species, cov = A)) ,
data = dataset_all_species_phylogeny,
family = bernoulli(),
#prior = prior,
data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(brm_island_2)
summary(brm_island_2)## Family: bernoulli
## Links: mu = logit
## Formula: bin_island ~ 1 + polymorphism + log(bole_female) + (1 | gr(species, cov = A))
## Data: dataset_all_species_phylogeny (Number of observations: 113)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Group-Level Effects:
## ~species (Number of levels: 113)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 5.41 6.37 0.82 18.38 1.00 3502 3558
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.25 7.06 -16.55 4.67 1.00 8697 4282
## polymorphismyes 4.94 4.58 1.27 14.84 1.00 5486 3842
## logbole_female 2.47 2.92 -0.20 9.08 1.00 6401 3984
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_island_2)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.573 (95% CI [0.187, 0.922])
## Marginal R2: 0.063 (95% CI [1.059e-25, 0.388])## Check if the predicted values fits the rawdata
pp_check(brm_island_2)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
##Preliminary plots
#plot(conditional_effects(With this dataset there seems to be an association between colour polymorphism and the presence on islands
## .
## 0 1
## 0.472 0.528## .
## 0 1
## 0.1803279 0.8196721
A similar pattern is obtained when with run the model without the phylogeny
set.seed(30011994)
brm_island_3 <- brm(
bin_island ~ 1 + polymorphism + log(bole_female),
data = dataset_all_species_phylogeny,
family = bernoulli(),
#prior = prior,
#data2 = list(A = A),
control = list(adapt_delta = 0.999, max_treedepth=10)
,chains = 4, cores = 4, iter = 20000
)## Warning: Rows containing NAs were excluded from the model.## Compiling Stan program...## Start samplingpairs(brm_island_3)
summary(brm_island_3)## Family: bernoulli
## Links: mu = logit
## Formula: bin_island ~ 1 + polymorphism + log(bole_female)
## Data: dataset_all_species_phylogeny (Number of observations: 113)
## Draws: 4 chains, each with iter = 20000; warmup = 10000; thin = 1;
## total post-warmup draws = 40000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.03 0.87 -1.76 1.67 1.00 23009 22546
## polymorphismyes 2.21 0.83 0.79 4.05 1.00 14062 13034
## logbole_female 0.48 0.42 -0.32 1.33 1.00 21317 20839
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#r2
r2_bayes(brm_island_3)## # Bayesian R2 with Compatibility Interval
##
## Conditional R2: 0.106 (95% CI [0.027, 0.197])## Check if the predicted values fits the rawdata
pp_check(brm_island_3)## Using 10 posterior draws for ppc type 'dens_overlay' by default.
9 Conclusion
Lets observe how polymorphic and monomorphic species differ according to all the predictor. To build this graph we will use the linear models with the total data set and the Island model with the highest number of species.
all_models<-NULL
for(mod in c("brm_latrange_1","area_polygon_1","eco_reg_points_1","eco_reg_polygon_1","temp_zones_polygon_1","temp_zones_points_1","brm_island_2")){
baye_mode = get(mod)
bayes_results<-baye_mode %>%
spread_draws(b_polymorphismyes)
bayes_results<-tibble(b_polymorphismyes=bayes_results$b_polymorphismyes,model=mod)
all_models<-bind_rows(all_models, bayes_results)
}
all_models$model<-factor(all_models$model,levels=c("brm_island_2","temp_zones_polygon_1","temp_zones_points_1","eco_reg_polygon_1","eco_reg_points_1","area_polygon_1","brm_latrange_1"))
na.omit(all_models) %>% ggplot(aes(y = model, x = b_polymorphismyes, fill = after_stat(x < 0))) +
stat_halfeye()+
theme_classic()+
geom_vline(xintercept = 0, linetype = "dashed",col="black",size=0.8)+
labs(x="Estimate",y="Models")+
xlim(-0.5,5)+
scale_fill_manual(values = c("#BCCAEF","#D66D79" ))## Warning: Removed 12885 rows containing missing values (`stat_slabinterval()`).
From all the variables and data filtering explored, we can conclude that monomorphic and polymorphic spider species in our dataset only differ in their presence on islands